(Cross-posted from WBGO.org. Thanks to Nate Chinen for inviting me to write this.)

With most things, I’ve found, what’s most interesting isn’t the thing in itself, but rather its relationship to other things. In other words, everything is relative, which is why I was so excited to see the video below. It shows, using harmony, rhythm and visuals, the relationships between the orbits of the seven planets around TRAPPIST-1, a dwarf star about 40 light years away from us.

The video was made by astrophysicist Daniel Tamayo, who worked out the planets’ orbits, and Matt Russo, a fellow scientist who also plays jazz guitar. Musician Andrew Santaguida contributed as well.

What’s going on here? Why does it sound so good? How, in the first place, were these orbits figured out? It’s only in the past 25 years that we’ve been able to detect planets in orbit around stars other than our own. This is mainly done indirectly, by — for example — measuring faint dips in a star’s brightness as planets pass in front of it. In 2015, using this technique, three exoplanets, as planets outside of our Solar System are called, were discovered orbiting around TRAPPIST-1, a dwarf star about 40 light-years away from us in the Aquarius constellation. In February 2017, four more were discovered. The field of exoplanet detection has gotten so advanced that scientists are able to determine not only the size and mass of these planets, but also their orbital periods and — most amazingly — chemical composition. Three of TRAPPIST-1’s planets are considered to be within its habitable zone, where life could potentially be sustained, and some of the planets may even have liquid water on their surface.

Artist Impression of the TRAPPIST-1 system (NASA/JPL)

This is remarkable enough already. But what makes the TRAPPIST-1 system even more special is the relationships between its planets’ orbits. The farthest planet completes one orbit every 18 Earth days, and the next farthest once every 12. What’s 18 divided by 12? That’s 1.5, or 3/2. In other words, in the time it takes the farthest planet to go twice around the star, the next farthest has gone around three times.

We hear sound when the air around us vibrates and those vibrations reach our ears. Vibrations are a bit like orbits — they repeat at a certain frequency (the note A in the middle of a piano, for example, vibrates 440 times per second). What does it sound like when sounds vibrate in that same 3/2 ratio, one sound vibrating twice in the time it takes the other to vibrate three times? As Pythagoras discovered long ago, it sounds lovely. The musical interval which results, the so-called perfect fifth, is one of the fundamental building blocks of harmony — and not only Western harmony. It turns up in traditional music from all around the world, in every possible key. It sounds like this:

Now let’s look at the closest planet to TRAPPIST-1. It orbits the star in only 1.5 Earth days (these orbital periods are short because the system is very compact — all seven planets orbit the star much closer than Mercury orbits the Sun, and the star itself is only about the size of Jupiter). The next closest goes around once every 2.4 days, which gives their orbits a relationship of about 8/5. Now, if one sound vibrates eight times in the time it takes another to vibrate five, we get the interval of a minor sixth, which sounds like this:

This is a less basic interval than the perfect fifth, but it’s still part of the fundamental material of music. Like the perfect fifth, it’s a consonant interval, meaning its sounds seem to belong together; the relationship sounds harmonious to our ears. Let’s pause here for a moment to consider what we’re talking about: that some planets orbiting a star unfathomably far away from us are doing so in a way that sounds good to us. Isn’t that something?

What’s more, we’re capable of hearing relationships like 3/2 and 8/5 in other ways than through harmony. As I’ve written about before, pitch and rhythm are the same thing, expressed at different time scales. We can hear 8/5 as an interval between two pitches, and we can also hear it as a rhythm in which one sound is played eight times in the time the other is played five:

8 / 5 in musical notation

What does this rhythm sound like?

Pretty catchy, I would say! What’s important to appreciate is that this is exactly the same as hearing a minor sixth as harmony, only about 200 times slower. Pitch and rhythm are simply two different ways for us to perceive frequency relationships. It’s even possible to experience one turning into the other, and back again:

With the TRAPPIST-1 system, it’s not only the inner and outer two planets that orbit in a resonant harmonic relationships. All seven, surprisingly, do — the only planetary system discovered so far with such consistently resonant orbits. Their relationships, from inner to outer, are very nearly as follows: 8/5, 5/3, 3/2, 3/2, 4/3, and 3/2. This works out to a combined 2 / 3 / 4 / 6 / 9 / 15 / 24. Let’s hear all of these together, built up from the outermost planet to the innermost, in music:

Pretty, right? Now let’s hear these same relationships as rhythm, but instead of playing each note with a percussive sound as we did before with the minor sixth, let’s express each with the pitch that results from the orbital relationships. For fun, here it is in musical notation:

We’re now hearing the TRAPPIST-1 system as pitch and rhythmic relationships, simultaneously. We’re experiencing the same thing in two different ways at once. As a friend of mine pointed out, it’s a bit like tasting roasted cauliflower next to a cauliflower gratin on a bed of cauliflower couscous.

Cauliflower gratin

But wait, something’s off — if you’re listening closely, you may have noticed that this is quite a bit more in tune and in time than the sounds and rhythms played in the video at top. This is because, although the TRAPPIST-1 system has relationships that are very close to whole numbers, they’re actually a little off. Nature is funny that way. The outermost planet doesn’t orbit in exactly 18 days but rather 18.766. The second farthest planet goes around in 12.353 days rather than 12. So their relationship isn’t quite 1.5, but rather 1.51918. We’ve been listening to an idealized version of the system so far. Let’s see what the real thing sounds like, with the most precise orbital periods plugged in, first as pitch, then as pitch and rhythm:

It still sounds quite harmonious, if a little sour (it’s worth comparing to the two previous recordings above). The discrepancies are particularly noticeable in the rhythm, which doesn’t line up quite as neatly as before. The intervals making up the harmonies aren’t as clean, either, but they still “work” — we still hear a clear, quite consonant chord (the history of tuning systems tells us that there is always a little lee-way with tuning). One result of recreating this rendering for myself was to notice that there is a wobble, or vibrato, in the piano-like sound that the TRAPPIST-1 physicists used in their video. To my ears, this causes the harmonies to sound a little further out of tune than they actually are. I’m using simpler, more stable sounds in my own rendering.

So — TRAPPIST-1 is remarkable. Without interfering with its orbits in any way, by just presenting the data scaled up to our range of hearing, we hear what we readily identify as harmonious music. But how special is it? To compare, I wanted to listen to our own Solar System. From Mercury’s 88-day orbit to Neptune’s 165-year one, our home planets take a lot longer to orbit the Sun than TRAPPIST-1’s do. But their relationships — Earth to Mars relate by about 17/9, for example — can be rendered in music just as well.

The Solar System (distances not to scale — WP)

The Solar System is so spread out that it helps to break it up. Let’s begin with the four inner planets, Mercury, Venus, Earth and Mars. Heard on their own, they spell out an eerie kind of Major 7th chord:

Meanwhile the outer planets Jupiter, Saturn, Uranus and Neptune together have something of a half-diminished color:

Now let’s try to hear these together. Because it is so compact, the planetary system of TRAPPIST-1 can fit neatly into the range of frequencies where we comfortably hear harmonies. Not so for the Solar System. TRAPPIST-1’s innermost planet makes only 12 orbits in the time the outermost makes 1, whereas Mercury makes 684 in the time Neptune makes 1, a vastly greater range that stretches our hearing to the limits. If I assign an extremely low note to Neptune, a low 23Hz rumble right at the bottom of our audible range, that puts Mercury’s sound right at the top of what we can hear, a mere dog whistle at 15,736Hz — which younger listeners will have more success hearing than older ones. Even if we’re able to hear this, we just don’t have the perceptual capacity to hear real harmonic relationships between tones spread that far apart.

For that reason, I’ve transposed the inner four planets down by 2 octaves, and the outer four up by 1 octave. As you’ll remember from music theory class, if you were there, this doesn’t alter the resulting harmony (think chord inversions) — it just allows us to hear it. Here is the sound of our Solar System, from Neptune through Mercury:

There’s no doubt when we hear this that the Solar System isn’t anywhere as harmonious as TRAPPIST-1. Not even in the same ballpark. I actually like the sound that results — it has a mystery that I find enticing — but it’s wildly dissonant. While there are some near-resonances in the Solar System — Uranus makes nearly two orbits in the time it takes Neptune to make one, for example — most of them are too far out of tune to qualify as harmonious.

The fact that the TRAPPIST-1 orbits are so obviously harmonious in comparison tells us something important about the physics of the system. The planets are so close together that they would collide with each other if they hadn’t settled into these resonant orbital relationships. Meanwhile, the planets of the Solar System are far enough apart that they face fewer demands on their orbits.

Kepler’s Harmonices Mundi

The great astronomer Johannes Kepler, in addition to contributing enormously to the field of astronomy in the 17th century, was also something of an astrologer. He was particularly interested in how a planet’s speed varied during its orbit, which is what he rendered in musical notation in the figure above. He believed that the happiness of life on Earth depended on how harmoniously the orbits of the planets related to one another. He was following in the footsteps of the ancient Greeks, who advocated for a Harmony of the Spheres over 2,000 years ago. It turns out people have been trying to listen to planetary orbits for a very long time; it’s remarkable that we live in a time where we can accurately listen not only to our own, but to planets around other stars as well.

Aristotle and Kepler would have had to believe that life in the TRAPPIST-1 system, if indeed there any, is pretty dandy. It’s hard to imagine a system with more harmonious planets. Or is it? I’ll leave you with a sound rendering I made of the four Galilean Moons of Jupiter, both in pitch and rhythm. Io, Europa, Ganymede and Callisto have orbits that are perhaps even more harmonious than those of TRAPPIST-1, with a beautiful minor key sonority. Three of the moons are in quasi-perfect octaves, a 2 to 1 relationship that is the simplest there is. I guess life must be pretty good there, too.

I’ve got a little time off from touring so I’m cleaning house. While sorting through old papers I came across the interview below. Most of these answers still ring true to me today. It’s fun to hear from past iterations of oneself, sometimes.

Jazz Inside: Can you talk about how your unique childhood/young adulthood might have influenced your voice as a musician? You were born in Paris, France to American parents, got a degree in astrophysics in Edinburgh, Scotland and then moved here.

Dan Tepfer: I grew up in a way that doesn’t really give me any choice but to see the outside view, to see music as a pluralist art form. My grandfather was a jazz pianist on the West Coast. As a matter of fact, Nancy King, Ralph Towner and Glen Moore credit him with getting them into jazz. My mom is an opera singer. So I grew up hearing a lot of music, mainly jazz and classical, from before I was even born. I studied classical piano at one of the Paris conservatories through my childhood and teens, but somehow I always mainly considered myself an improviser. Knowing that my granddad improvised made it okay to do that in my mind, despite what my classical teacher would say. Playing classical music, even though I secretly really enjoyed it, and still do, was my work; improvising was my fun, so I ended up spending a lot of time at the piano making things up. And that’s basically how I learned jazz. I’m mainly self-taught except for a few lessons growing up and a two-year master’s degree in jazz from the New England Conservatory; but most of my foundation had already been set by then. So, because for most of my life nobody told me how to play jazz, it’s always felt natural to me to view it as just ‘improvisation’, to be really open-minded about it from a stylistic standpoint. Astrophysics is one of the most fascinating subjects there is to me, but I realized fairly quickly that as a full-time occupation, it wasn’t going to beat the combination of the visceral and intellectual involved in making music.

JI: How did music become such a big part of your life?

DT: I can’t ever remember it not being the biggest part of my life. It’s something that’s always been a given for me, for some reason. I’ve been passionate about other things — astrophysics, rock climbing, even computers, but music has always been the through-line, the wise friend with the unconditional love that I can always turn to. As I said before, my mom is an opera singer and for the nine months before I was born she was belting her lungs out five nights a week with me in her belly, so that might have something to do with it…

JI: What is your life like in New York? How do you make it all work in these expensive times?

DT: When I first moved to town I did all kinds of things to stay afloat. I taught French, I designed websites, I accompanied dance classes, I did voice-overs for language tapes, I taught three-year-olds piano, you name it. Then, starting in 2006, I got lucky and won some piano competitions, which gave me a little financial cushion to weather the lean times. It also allowed me to buy a piano. Since then I’ve been able to make a modest living playing music, which I’m extremely thankful for. My costs are low; I was recently joking to a friend that I have the least responsibilities I could possibly have in my life. I’m not married, don’t have any kids, don’t have a car, don’t own any property, don’t have any pets; my rent is pretty low and aside from watering a couple plants in my apartment, basically my only responsibilities are to myself and music. I live in Lefferts Gardens, in Brooklyn, on the East side of Prospect Park, an area that houses an astounding number of jazz musicians, and those two things —the Park and the creative stimulation all around — make my life a lot happier. When I’m not in New York I’m on tour as a leader — I have solo and trio projects that have been getting a nice amount of road time — or as a sideman.

JI: What motivates you and drives you forward on your journey?

DT: I don’t know. That’s perhaps the fundamental question about life, isn’t it? Why are we all doing it? Why are we even trying? In the end we’re all going to die anyway. And even if you believe in the importance of Humanity, beyond individuals, lasting into the future, you can’t ignore the fact that at some point down the line — okay, way down the line — the Sun is going to become a red giant and engulf the Earth. But that’s the rational mind talking. At an intuitive level I find myself thirsty for learning and expression. I’d love to find out how creative I can be. I also know that becoming an artist is essentially the process of getting to know yourself, of resolving, or at least becoming conscious of, your inner contradictions, and that’s a deeply attractive path to me. I don’t know why that is, and that’s kind of the beauty of it. I’m definitely at my most creative and free when I can manage to get a good grip on how futile the whole operation is anyway. It’s kind of a wonderful feeling, the realization that we’re really just doing it for the fun of it, because we feel like it. Art, to me, is fundamentally an expression of that, the mysterious human need to document our existence on Earth by leaving behind an expression of our own unique sensitivity: it has no justification but itself; we like it because we like it.

JI: Can you talk about the process of composing for you? How do you approach this task?

DT: That’s a tough one. Composing is hard for me, and I take comfort in knowing that it also is and was for some of the great musicians that I admire. One of the best ways for me to write is right before a jam session: I’ll sit down about an hour before the session is supposed to start with the simple goal of writing something down, whatever it may be, that we’ll be able to play together on the session. l’ve written some of my best tunes this way. It helps to know who I’m writing for. After more than fifteen years of composing, I finally feel like I have some kind of philosophical grip on what composition is: it’s the process of finding sounds that you like and writing them down so that you can remember them. *Like” is the important term here. Nothing else really matters — the theoretical constructs, etc., are nice for building an underlying architecture, but ultimately the only thing that matters is whether you dig it or not. So I try to stay really close to that feeling: if I’m writing and something pops into my head that sounds good to me, I rush to write it down before I second-guess it. And sometimes a tune just pops down, fully formed, from God-knows-where and you write it down. But you can’t count on that. Right now I’m writing a piano concerto for myself and the Prague Castle Guard orchestra in Czech Republic that we’ll premiere in May. It’s my first time writing for orchestra, and it’s daunting! But I love feeling challenged.

JI: What is it about musical improvisation that you find so valuable? What does it offer to you, your band-mates, and the listeners? What motivates you and drives you forward?

DT: That’s an excellent question. Why improvise? Why not just plan everything out ahead of time? Aside from the obvious answers — it’s less work, it makes it different every time, it’s more fun, etc. — I think it fundamentally has to do with desire. Desire in the sense that in all great music, there’s a palpable desire, a need, an intent, behind every note. With written music it takes a truly brilliant performer to be able to muster up that desire for every note when the notes were written by someone else. That’s what makes lesser performances of Bach so boring — all we hear is a bunch of notes. But when Glenn Gould played Bach, for example, he could somehow make it sound like he was creating the music as he was playing it. With improvisation, there’s no reason to play a note unless we deeply desire it. We can just lay out if we want to. So we have the opportunity to create music where every note we play comes from a clear intent — on a bluesy day we can play darkly, on the day we fall in love we can play with pure joy. When music has desire behind every note, it can be unbelievably powerful, and I think improvisation maximizes the possibility of that happening. This isn’t a guarantee, of course — even in improvisation, it’s perfectly possible and pretty common, especially since the advent of jazz education — to play superfluous notes… But at least the possibility is there.

JI: As an artist, your state of mind and ability to dig deep is important. Outside of playing, what do you do to re-center and find peace of mind? What do you do to break through all of the surface stress in our contemporary world? Or perhaps, you feel that angst is good for music?

DT: I think my single deepest source of perspective is Nature, mountains especially. I used to be a fairly dedicated rock climber and mountain climber; nowadays I don’t get out as much as I’d like but I did manage to climb Mount Rainier, outside of Seattle, this summer, with an old climbing buddy. We took a little-traveled route to the summit that really got us away from everything. There’s this completely obvious timelessness and majesty about mountains that you can’t possibly ignore, and there’s nothing like them, to me, if what you’re looking for is some perspective. It’s always a dance between spending time deeply involved in the Work of music to the point of creative exhaustion, then re-filling the tanks with the help of a wide-open view.

I left the movie theater last night, post-Birdman, intensely moved. Rarely has a film gotten to me so directly. Birdman is a wacky movie that seems to be asking a serious question: why live? What keeps us trucking on and floundering and trying as hard as we can to accomplish things, when we’re only specks of dust on a small rock orbiting around an average star, one of billions in a galaxy that itself is one of billions in the universe? How can you explain that we care so deeply about our shit? Our little troubles and tribulations? The movie has a simple answer: madness. That’s what explains it. And the beauty of it all is that madness is at once a curse and a necessity, without which, well, we might as well throw in the towel.

In one scene, Riggan Thomas (Michael Keaton), an aging Hollywood actor trying to make a grand artistic statement on Broadway, asks his daughter (Emma Stone) about the thousands of small dashes she’s been drawing on a roll of toilet paper. It’s a trick she learned in rehab, she explains, each of the dashes representing a thousand years, the entire roll representing the age of planet Earth (4.5 billion years), and the last toilet paper square standing for the amount of time (about 150,000 years) that modern humans have been around. The lesson: let’s step away from ourselves for a moment and contemplate how small we are. Let’s reevaluate. Riggan responds by absent-mindedly wiping the mustard off his mouth with the square representing humanity (the daughter: “You just wiped out the entire human race!”). Sure, we’re small and our selfish focus on our own small troubles looks ridiculous from any real perspective, but who cares, really, when it’s all that’s in front of your nose?

In another scene, our hero walks by a man on the street declaiming Macbeth:

[Life] is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.

In the context of the movie, it’s easy to miss the fact that the choice of the excerpt here is important. I initially took it to be a scene about acting (which it also is), with a famous monologue thrown in for good measure. But it’s not just any old monologue; it’s the classic line in which Shakespeare makes his strongest statement about the absurdity of existence—or at least, how absurd it all seems if you believe in nothing. Riggan has a piece of paper taped to his dressing-room mirror that reads “A thing is just a thing, not what is said of that thing”—basically a Buddhist sentiment that we see Riggan trying to honor through meditation and breathing exercises. He tries hard to ignore the narcissistic voice in his head. And yet, in the ultimate irony, it’s a New York Times review, at the end of the movie, that settles the question of whether his play is any good or not. We have no idea until then one way or another, and no-one else seems to have any idea either. Perhaps the only important thing about a thing is what is said about it? It’s a messy world, folks.

Speaking of messy, how about the scene where the screenwriters bring two of the classic performer’s nightmares together? I’ve had both of them, many times: in the first, you know you’re supposed to be on stage but you can’t find it (see Spinal Tap—they had it too); in the second, you’re on stage and you realize you’re only wearing underwear. Riggan is subjected to both, in a plausible real life scenario, at once. Oh, the humiliation! And oh, the fine line between total embarrassment and greatness—there’s nothing more riveting than a human being doing all he can to transcend humiliation, specifically because we, who are watching, know that the success of the effort is entirely predicated on whether we feel it’s successful or not—i.e. on what we will say about it. It’s a moment of total power for the audience—the power of judgement. And perhaps this is what’s lacking from a lot of music I hear today, particularly in jazz—where is the risk? Where is the potential humiliation, to be battled with? And in the absence of the potential for total failure, what’s really in it for the audience? Shouldn’t every performance be a retelling of the story of Icarus (hopefully with a happier ending)?

Madness. What would we do without it? The film is quite clear on this point: people wouldn’t make much art. To make art is to believe that things matter; that we ourselves matter, when much around us is telling us the opposite (speck of dirt on rock around the Sun, etc). This recalls the great line from Moby Dick:

You is sharks, sartin; but if you gobern de shark in you, why den you be angel; for all angel is not’ing more dan de shark well goberned.

I.e. it’s not a matter of suppressing the shark within us, but a matter of managing its energies. In the same way, the schizophrenic voice in Riggan’s head seems to be the plague of his existence, but it’s ultimately what leads him to give a performance where he actually “risks all” (his life), and which lands him the all-vindicating New York Times rave. The last scene is particularly telling on this point: at first it seems that his near-death experience has enabled him to finally leave his narcissism behind, a shift visually represented in the film by Riggan’s ex-action-hero persona meekly sitting on the john. Our expectation, at this point, is that our hero has finally seen the light and will from now on live in the land of reality, not some desperate and self-destructive clinging to “being great.” Not so. The very end of the movie refuses to do away with madness, and in fact embraces it anew, and for the first time in a way that other characters in the movie can see as well. Perhaps Riggan has finally managed to make his madness his own—to govern his shark.

For life is ultimately absurd. If we know we’re going to die, then why live? Because we want to, that’s why. And there’s no explaining that desire, beyond the fact that eons of evolution have selected for the organisms that most want to survive. Schopenhauer* said

Man can do what he wills but he cannot will what he wills

and that is, to me, one of the most profound things that can be said about our existence. You can do what you want (if you’re lucky), but you can’t decide what you want. Somewhere in the mystery of our desires—of why we want certain things and not others—lives the concept of God. And Birdman, by exulting in the absurdity of our existence, manages to be one of the most profound movies I’ve seen.

It’s also very funny, viscerally compelling (I was on the edge of my seat for much of the movie), technically stunning (most of the film appears as a single long shot, although it’s not actually), and has great performances throughout. I loved the many abrupt shifts in tone as the movie progressed, many of them registering only as changes in an actor’s face. Most were overtly theatrical, perhaps even overdone by film standards, but this is a movie that is very much about theater. Early on, Riggan’s actress girlfriend breaks the fourth wall and summons us, the audience, into the play’s opening night in a way that directly recalls A Midsummer Night’s Dream‘s Puck. Shakespeare is never very far away here.

A word about the music. Aside from a few 19th-century orchestral excerpts, it’s all Antonio Sanchez playing drums, unaccompanied. Although that may sound unpromising on paper (unless you know Antonio’s playing—he’s one of the best jazz drummers around), it is highly effective film music. I wrote my first feature film score in early 2014 (for Alexis and Bodine Boling’s Movement And Location) and the first thing I learned was how powerful film music is. It can singlehandedly set the emotional tone of a scene. It was a revelation for me, because in the music I normally write, I think mostly about the structure and language of the music, not its affect, in much the same way that as I’m writing these words, I’m not thinking about how you, the reader, are going to feel while reading them—I’m only trying to convey some ideas. The emotion the music carries is something that emerges after the fact, on its own, not something I purposely craft. This is turned on its head in movie music, and that’s probably why most film scores are conservative from the perspective of their musical language: what’s essential is to convey emotion, so the most accessible language is often used to make the communication of that emotion as efficient as possible. What I was reminded of, watching and listening to Birdman, is how the emotional impact of music is itself a mysterious thing. How is it that Sanchez’s drums, those pitch-less hits and sizzles, can convey such a wide range of angst, anticipation, mulling, self-loathing, catharsis? How does that come through? It does, somehow. There’s no recipe for emotion in music. The surest bet is probably, if you’re the performer of the music, just to try to feel the emotion yourself, and trust that it will somehow be conveyed to the viewer—a process that sounds a lot like the work of an actor.

*the internet is great. I always thought that line was from Einstein, but looking it up just now, it turns out he was quoting Schopenhauer, whom I’ve never read, when he said it in a 1929 interview.

As I look back over the last ten years and the peculiar journey with J.S. Bach that the time represents for me, it’s sometimes hard to believe that I’m here, now, playing the Goldberg Variations from memory in their entirety, for sometimes sizeable audiences, well enough apparently to get enthusiastic approval from the classical section of the New York Times. I’m really a jazz pianist, after all, and the Goldbergs are hard. And the crazy thing is that I never set out to do this in the first place. How did I get here? The best answer I can give, to echo an experience many musicians have reported through the years, is that Bach taught me.

I grew up in Paris, France, in an American family, and started studying piano at the local conservatory when I was six. I was never asked what I wanted to play, as some of my friends in the US were—playing TV themes wasn’t on the radar. Mostly, I was made to play Bach, lots of it. At the same time, following the example of my grandfather, a jazz pianist on the West Coast, I started improvising, and that mode of music-making quickly took over my fledging artistic identity, even as I kept going through the classical repertoire with my teachers at the Conservatoire.

So I grew up with solid classical training paired with an all-out obsession with jazz and improvisation, which I mainly taught myself. In my early teens, I discovered the Goldberg Variations at a friend’s house in Paris, as recorded by Glenn Gould in 1981, and they took hold of me then like the most beautiful and tenacious earworm. Still, it was only in my early twenties, while studying jazz at the New England Conservatory, that I got a score, and even then, it took me a long time to look past the Aria. Slowly, out of what felt like simple curiosity, I started learning a Variation here and there, in breaks between practicing jazz scales. By the time I moved to New York, in ’06, I had learned the first five, at most. And yet, even as I put all my efforts into breaking into the New York jazz scene and developing a personal voice as an improviser, the Goldbergs stuck with me. I kept coming back to them, and found a classical teacher, Zitta Zohar, who convinced me they were somehow within reach.

The jazz pianist Fred Hersch, a long-time mentor of mine, recently reminded me that he had asked me, back then, why I was spending so much time learning the Variations, music that I would presumably never perform. Apparently I answered, “I don’t know—it just feels like something I have to do”. And so I soldiered on, slowly and not all that surely.

Meanwhile, my jazz career was developing. I got a boost from the American Pianists Association’s Cole Porter Fellowship, a competition prize that included a fair amount of touring. And so it was that I found myself backstage at a small concert hall in Czech Republic in early ‘08, fifteen concerts into a twenty-day solo tour, nearing creative exhaustion. I had decided for some reason that the gigs should be freely improvised, and I was starting to run out of ideas. So I decided to use the Goldbergs as inspiration: I played the first four or five, and followed each one with long, freeform improvisations that used the spirit of the preceding variation as a jumping-off point. The audience’s reaction surprised me—I walked off stage feeling that something special had happened. So I tried it again the next night. Bach’s genius suddenly struck me hard: instead of panning for gold dust in a cold and barren stream, which is how it increasingly felt to make improvisations up out of nothing, using the Goldbergs as inspiration was like starting with a giant gold nugget in my hand. Each one had such an utterly distinct identity. Suddenly my improvisations, though still totally speculative and fanciful, had as their subject something very specific, something rock-solid and strong.

And so my improvising started to teach me about Bach. Back home, as I turned to him again with renewed enthusiasm, I wanted to know why it was that each of his short pieces felt so entirely of a piece. The answer—Bach’s extreme compositional economy—took a long time to reveal itself to me; strangely, it didn’t jump out at me at all when I was just learning to play the pieces. And yet, to take an early and simple example, Variation 2 introduces a motive in its first half that gets repeated nearly verbatim in every single bar of the second half, this motive itself being derived from the oscillating bass-line figure that repeats throughout. I can only describe Bach’s strategy for saving the piece from predictability as sleight-of-hand: like a skilled magician, he continuously directs our attention away from the obvious. The clockwork machinery hides in plain sight.

He uses misdirection throughout the Goldbergs, in fact. Where a lesser artist might have wanted to make his achievement in devising a series of canons at every interval from the unison to the ninth clear to the listener, Bach often seems to do everything in his power to hide it, even as he never breaks from strict canonical form. Besides the continuous overlapping and crossing of voices, which is its own form of disguise, there’s a wonderful moment in Variation 12 where the third voice, which is free and not subject to canonical rules, steals the thunder from one of the 2nd voice’s entrances by playing its melody a third away, a beat early.

Only the least pedantic composer would do such a thing. And this is in a canon at the inverted fourth, where a listener’s chances of anticipating the canonic response are even lower than in the non-inverted ones! An advanced volleyball-like fake-out is being deployed against an opponent who couldn’t possibly return the ball if he tried. Bach, I slowly realized, had his cake and ate it, too: his structures, if you look, are as plain as day and as solid as the steel skeleton of a modern building, and yet we rarely, if ever, notice them (as we often do, for example, in Handel). We only hear the incredibly expressive melodies, the rhythmic inventiveness, the continuous small surprises. Has a rule-follower ever been less boring than Bach?

By the summer of ’09, I had worked up enough courage to play eight of the Variations, followed by improvisations, at a small solo concert in Paris. I had been studying Zen philosophy and believed wholeheartedly that an improvisation should have integrity, as a piece of music, if I only put myself in an unobstructed frame of mind and let it flow, as it were, out of me. And the audience, for the most part, was convinced—it felt, again, like something special was happening, that I was exploring fertile ground.

But something started to gnaw at me: was it truly right, when Bach was being so phenomenally economical and elegant, to respond in such a freewheeling way? What would happen if I started to borrow some of his structure, too, beyond his emotional leads?

In the fall, I had a small solo tour through the Midwest, and played the Goldbergs on every gig. This strange idea—of following one of the most perfect works of art with quite imperfect improvisations—was starting to crystallize in my mind as something that had a certain legitimacy, partially as a result of personal conviction, but also because of the encouragement I was getting on the road. (I would later learn that the idea of improvising off of the Goldbergs wasn’t new: John Lewis and Uri Caine, among others, had recorded their own treatments of the theme in different ways.) Still, a year went by before I started thinking seriously of recording it. In early ’11, after releasing a jazz piano trio album of original material and writing a concerto for piano and wind symphony, I happened to meet Bonnie Barrett, the director of Yamaha Artist Services in New York. I became a Yamaha artist and saw an opportunity: if I brought in my own recording gear, I could use the Yamaha showroom in Midtown Manhattan to make my solo record with virtually unlimited studio time. As much as I’d been performing the music in public, a part of me realized there was still a lot of work to do. I just didn’t know quite how much.

To make a long story short, I recorded what eventually became Goldberg Variations / Variations three times. Once as I’d been performing it, with fewer than half the Variations and long, rambling improvisations. Then, when I realized presenting only part of a work so whole as the Goldbergs to the world would be an embarrassment, as a much-too-long and obscure investigation into all the Variations, with a non-linear structure and a speculative tone throughout. And finally, once I realized that the purity and coherence of the Goldbergs called out for the most simple and clear structure possible, the way it finally ended up, with each of the 30 movements alternating with an improvisation of similar length, closely linked to the preceding Variation.

Since I essentially learned to play the second half of the Goldbergs while I was recording it, I started to think of the project less as a record of a live performance and more as a conceptual work that might end up only existing as a recording. There are, after all, many electronic and pop artists who never perform their work live. Recorded music can be a destination of its own.

The recording process was a powerful learning experience for me. Suddenly my weaknesses of articulation and phrasing, when I played Bach’s notes, couldn’t be ignored (as they could so easily when I practiced at home, or even when I performed). Alone in the Yamaha space, often late into the night, I recorded take after take of the Variations, and didn’t shy away from editing the best portions together. Glenn Gould did plenty of editing, I reasoned, so why couldn’t I? (I conveniently ignored the fact that he, at least, was more than capable of performing the work in front of an audience.) Similarly, the recording process brought out all the structural, emotional and technical faults of my improvisations. It became clear to me that the only way they could hope to stand up next to the beauty and perfection of the Variations was if they lost most of the indulgence I’d been allowing them to have. They needed to be concise and focused; they needed to get to the point, all while remaining personal. I started to develop explicit strategies. I realized, for example, that I was capable of improvising my own canons, as long as I kept them fairly rudimentary. I realized that many of the virtuosic Variations stemmed from a very restricted amount of material, and tried to find ways to improvise with a similarly limited set of ideas. I saw that Bach gave himself considerable license in the way he navigated the I-I-V || V-vi-I harmonic framework that all the Variations share, and let myself take my own varied pathways through the changes. I researched the last Variation, the Quodlibet, learned the words to the folk songs it uses as its melodic material, and substituted two jazz tunes I love as material for my improvised response. I gradually went from an implicit, alchemical relationship with the Variations to a much more precise and explicit one. And to my surprise, I gradually saw the project turn into something that felt like it had an integrity of its own.

It’s hard to record improvisations. There’s always the possibility that the next take will be better—it’s hard to stop. And yet as I recorded and re-recorded my responses to Bach, I began to recognize a flag that would occasionally go up in my mind, on good days, saying “this one’s good enough”. At first it was only one of my improvisations that felt that way, but I knew I had found a tone that rang true. My goal became to extend that tone, that feeling. I found it in another, then another, and later, in most of them (but not quite all). Saxophonist and producer Ben Wendel came in to help me choose the final takes, and suddenly I had a 62-track, 78-minute solo piano record that didn’t fit into any record-store genre category.

When it came out, at the end of 2011, I figured I would play a couple CD-release concerts and get back to touring with my trio or playing duo with saxophonist Lee Konitz, with whom my musical relationship had been growing. But to my surprise, critics either absolutely loved it (many of them) or loathed it with a passion (a few of them), and it started to take on a life of its own. After the Wall Street Journal ran a smart and generous feature, it even—surprisingly—started to sell.

For the album release, I played the full first half of the Variations for the first time, from memory, and it felt like the hardest thing I’d ever done in my life, like teetering on the edge of a precipice from beginning to end. I played the Paris CD-release gig at the Sunside, a small jazz club, and an agent heard me there who decided to take a chance on me. Soon he had booked a long fall tour for me in surprisingly large venues in France, and it dawned on me that it just wouldn’t be good enough to play only half of the record. I traveled to Cuba and for two and a half weeks studied percussion in the morning and memorized Goldbergs in the afternoons, away from cell phones, internet and acquaintances. An inexperienced performer of classical works, this was slow work for me, but I found it intensely rewarding. The act of memorizing forced me to make sense of the Variations, to organize them in my mind in a way that I hadn’t had to in the recording process. Bach’s economy became all the more apparent, as did the many-fold symmetries that govern the entire work, from the structural to the physical.

Bach was a lover of symmetry. If most of us can agree that symmetry is important in aesthetics—people tend to prefer symmetrical faces to asymmetrical ones—Bach took the idea to the extreme. At the physical level, in almost every variation as well as the majority of his other keyboard works, both hands get treated with exacting evenness, as if he wanted the interpreter of his music to fully appreciate the symmetry of the body, from the hands to the hemispheres of the brain. It’s not so much that the music is equally difficult for the left hand as it is for the right, although that’s part of it: it’s that to play Bach’s music well, one is obligated to bring the same amount of melodic consciousness to the left hand as the right. This is not the case in keyboard music by most other composers, which tends to heavily favor the higher register of the right hand. I’ve always resisted redistributing the voices of the Variations between the hands for this reason, even though it’s fairly common practice to do so in order to reduce hand crossing. To me, the feeling of bodily symmetry is an essential part of the experience of playing the piece.

At the structural level, the Goldbergs exhibit symmetries from the smallest to the largest scales. At the smallest, Bach is constantly playing with inversion, one example being the 16th-note runs that begin the first and second halves of Variation 26 above, strict mirror-images of each other.

At mid-scale, the rising or falling direction of the canonic intervals offers its own symmetries. Variation 24, for example, starts as a canon at the falling octave, switches to a rising octave on either side of its middle, and ends at the falling octave again, showing palindromic symmetry in its structure.

At the largest scale, the I-V || V-I binary form of the Aria and the Variations, with its central axis of symmetry, reflects the symmetry of the whole work, which similarly starts and ends in the same place (the Aria) and is split at its midpoint in the silence between the 15th variation and the 16th variation, the only to be titled “Overture”—a new beginning. The division of the Aria into 32 bars similarly reflects the work’s division into 32 movements, connecting the part to the whole. It’s easy to see this as an analogy of our existences: from ashes to ashes, with life in between. No wonder, then, that the Goldbergs are often described as expressing every possible shade of human emotion.

By the fall of ’12, I had coerced so many friends into letting me run through the program for them at home in casual performances—always with their share of little disasters—that I was beginning to get an idea of what I was up against. Performing the Goldbergs in public is not only a musical and spiritual challenge; it’s a physical and mental marathon, too. There’s no place to hide in Bach’s limpid music—it will immediately reveal and magnify any lapses in concentration, any tightening up of the body, any fear. And alternating between my role as interpreter of the written text and my role as in-the-moment improviser only made the task harder, constantly jolting me out of the possibility of getting ‘in the zone’ as I switched between mental states. To say I was terrified is an understatement, but the truth is that I’ve always been a thrill-seeker, in sports just as much as in music. So the terror had its own attraction. My dad called me an adrenaline junkie. And I think it’s fair to say that it’s during the fall tour that I started to learn what it really means to perform the Goldbergs in front of an audience. The tour was well received, but after I came home to Brooklyn, I heard Piotr Anderszewski play Bach’s English and French Suites at Carnegie Hall and was struck with a mirror-neuron-like physical feeling for how direct and unencumbered his relationship to the piano was. I realized that I had only fleetingly truly relaxed my body into the keyboard when I was playing Bach’s music on the road. A number of people had noted, in fact, how different my body language was between the Variations and my improvisations. The fear of a memory slip or technical slip-up kept my body on edge.

Much of my work since then has been on diminishing the sensation of fear. I realized, for example, that focusing my attention on rhythm and how it manifested in my body was a big help. It gave the notes a context to sit in and directed my attention forward, slightly into the future and away from the paralyzing present. I also realized the obvious, which is that the more I deepened my knowledge of Bach’s text, the more confidence I had when presenting it to an audience. Weeks after a solo performance in Vancouver, on the tail end of a duo tour with Ben Wendel, with whom I had just released a duo record, I got a call from an accomplished baroque harpsichordist who specializes in Bach and had heard my concert there. While he wished me good luck, he told me in no uncertain terms that my performance of the canons needed work. Why would you only bring out the top voice, he asked, when they’re all equally important? I didn’t have the heart to explain that I’d bring them all out if I could—that I was holding on for dear life out there. But I did take his cue and returned to Bach’s score with increased humility, practicing singing the interior voices of the canons while I played the others on the piano, or at other times willing myself to transpose variations to foreign keys from memory, and again at others spending hours obsessing over the exact phrasing of one short melody. Every time I opened the score, I was reminded that there is always something further to discover in Bach’s music—that the more you seek, the more you find. One thing dawned on me: when you’re starting with material of this quality, you don’t need to add anything to it. Your job is to get out of the way, to solve your interpretive problems so as to reveal the work itself as clearly as possible, like scraping mud off a diamond. I’m grateful to the pianist Simone Dinnerstein, a masterful interpreter of the Goldbergs, for generously giving me encouragement and musical advice during this time.

In the fall of ’13, a short solo tour came together on the East Coast, culminating in a show at one of my favorite New York venues, Le Poisson Rouge, a place that will present just about any style of music, from Johnny Gandelsman on solo violin to Laura Mvula with full band, as long as it’s good. Something happened on the tour—something started to click emotionally. I stopped trying so hard, started to let things be, both in the Variations and my improvisations. “Don’t try to make the music beautiful – it is beautiful; just let it out”, the beloved piano guru Sophia Rosoff had told me, and I slowly began to understand what she meant. And after the gig at Le Poisson Rouge, a man introduced himself to me, warmly, as Anthony Tommasini of the New York Times. A day later there was a glowing review in the paper, and suddenly the record was selling better on Amazon than Justin Timberlake and Lady Gaga, if only for a brief while. In the following days I got calls from some of the best presenters and festivals in America inviting me to perform.

What astonishes me about this is that the same critic, a fierce and erudite expert on classical music, may very well have panned me if he had heard me two years earlier. It took me that long to even begin to understand what was at stake when performing this music in front of an audience. And in those two years, my rising standards for what makes an acceptable performance of Bach started to spread laterally to the other types of music I was making, from my composing to my improvising. Dealing with Bach so frequently and—it felt—so intimately made all but the most well structured and meaningful new music feel lacking in comparison.

Looking back, as I prepare for solo shows at the Ravinia Festival, SF Jazz Center and Wigmore Hall in London, I’m amazed any of this happened at all. From many perspectives, I’m sure it would seem that I developed my Goldberg Variations / Variations project exactly backwards. But I didn’t know any better, and that’s probably why it ended up coming into existence—I just followed my nose. Above all, I’m grateful for the opportunity, a truly unexpected one for me, to engage much more deeply than I thought I ever would with one of music’s greatest geniuses, and to let Bach teach me.

Lee Konitz will be turning 87 in October, and his long and distinguished career as one of the most singular saxophonists in jazz needs no introduction (but if you need one, it’s here). He is known in particular for his intense focus on improvisational integrity, a desire for each musical choice to reflect the present moment as much as possible instead of a pre-made plan or habit.

It’s easy to overlook how radical this position is. In many other styles of music, from classical to pop, the goal in live performance is the opposite: to reproduce a carefully thought-out plan as faithfully as possible. Even in jazz, it’s not uncommon for groups to take a hybrid approach where a good portion of the material, even outside of written sections, is predetermined. Despite all this, Lee has somehow stubbornly insisted on showing up to his concerts prepared to be unprepared, and has (mostly) delighted audiences in doing so.

In my seven years of playing with Lee in diverse contexts I’ve been able to observe his commitment to the moment firsthand, particularly in our duo playing. One direct result of his approach is that his music is rarely boring; audiences seem to intuitively understand that something unique is going on; they pay attention in the way that people do when they genuinely don’t know what’s going to happen next.

And yet it’s also become clear to me that our audience doesn’t always necessarily understand what’s at stake when we perform. In his commitment to true improvisation, Lee isn’t taking the easy road. Failure is very much an option. And success, in the form of authentic engagement with the truth of the moment, may not sound like success to a listener used to being wowed by virtuosic effects.

I was reminded of this a few months ago when Lee and I played a duo concert in the Belgrade Jazz Festival. During the afternoon before the concert, I conducted a workshop with young local musicians. A number of them were very talented, but—as is common with young musicians—they had a tendency to play predictable patterns that weren’t closely related to what else was going on. As a result, I spent a lot of the workshop talking about the importance of listening and the goal of reacting as genuinely as possible to what we heard, rather than rattling off what we already knew.

In the audience were a couple of guys in their mid-thirties listening intently. After the concert, one of them approached me and told me that he had loved the concert, but that he might not have if he hadn’t heard my workshop earlier in the day. He explained that if I hadn’t clarified that our main objective on stage was to be as spontaneous and authentic as possible, he might have interpreted the opening of our concert as timid, rather than as a committed search for communication, and walked out. He was an electronic pop composer, and his job was to blow a listener’s socks off as quickly and reliably as possible. But, now that he understood the rules of our game, he found himself intensely engrossed in our concert, bringing his attention to how the notes that we played seemed to accord themselves with the feeling in the room at that moment, and the quality of the listening and communication between us.

I realized then how elusive the concept of real improvisation is. It’s a subtle thing that’s not easy to explain. As a listener, one could even be forgiven for asking what the point of improvising is in the first place. In the following interview, which I conducted for Chamber Music America at the very end of 2012, Lee and I explore this thorny topic, among others. I learned a lot from the conversation.

When I got back home to Brooklyn from tour a couple days ago, one of the things I did was buy Logic Pro X, a big update to a music production app I’ve used for a long time. To get a handle on it, I decided to make a track for a friend of mine. Earlier in the day I’d come across Bob Dylan’s All I Really Want To Do again, which, I was reminded, has got to be one of the most wonderfully simple and profound songs there is, and I thought it would do just fine.

I started hunting around the program for sounds. One of the big additions to Logic is that it now comes with a huge sample library. I focused on the orchestral samples, because I’ve never seriously tried to make a computer sound like a real orchestra before. The music I’ve made so far with sequencers, like my recent score for the film Movement & Location, is what we’d call electronic music: it purposely sounds machine-generated. There are people out there, particularly film composers, who are great at drawing acoustic-sounding music out of a computer, but it’s not a skill I’ve worked on before.

Logic now also has an advanced arpeggiator, which is something that was (amazingly) lacking in the old version — there were workarounds, but they weren’t pretty. In this context, arpeggiation means making melodies out of the notes in a chord by playing them sequentially instead of playing them all at once. Combine arpeggiation and some string samples, hold down a chord, and you might get something like this:

I just got home from a five-week tour in Europe and finally have some time to do what I call research. The way I see it, being a touring musician is a bit like being a scientist: you spend a bunch of time in the lab, and you find something that you’re excited about; then you have to go out and give a bunch of seminars to tell the world about it. But very soon you’re itching to get back to the lab, because you want to discover the next thing. So here I am, at home and doing research, which for me, right now, in between practicing piano and writing tunes, means getting into a computer music programming environment called SuperCollider.

Yesterday I was fooling around with it and suddenly realized that with SuperCollider, I could do something I’d been wanting to do for years, which is to make a recording of rhythm becoming pitch, and back again. You see, rhythm and pitch are exactly the same thing, only at very different speeds. How’s that, you ask? Well, let’s start with the harmonic series: